Question

Sin3x=sin2xcosx
помогите пж решить

Answer 1

$Sin3x=Sin2xCosx\\\\Sin(2x+x)=Sin2xCosx\\\\Sin2xCosx+SinxCos2x-Sin2xCosx= 0\\\\SinxCos2x=0\\\\\left[\begin{array}{ccc}Sinx=0\\Cos2x=0\end{array}\right\\\\\left[\begin{array}{ccc}x=\pi n,n\in Z \\2x=\frac{\pi }{2}+\pi n,n\in Z  \end{array}\right\\\\\left[\begin{array}{ccc}x=\pi n,n\in Z \\x=\frac{\pi }{4}+\frac{\pi n }{2},n\in Z\end{array}\right$